Problem: Solve for $x$ and $y$ using elimination. ${-3x-2y = -23}$ ${-5x-3y = -35}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-3$ ${-15x-10y = -115}$ $15x+9y = 105$ Add the top and bottom equations together. $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x-2y = -23}\thinspace$ to find $x$ ${-3x - 2}{(10)}{= -23}$ $-3x-20 = -23$ $-3x-20{+20} = -23{+20}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {-5x-3y = -35}\thinspace$ and get the same answer for $x$ : ${-5x - 3}{(10)}{= -35}$ ${x = 1}$